Question

In any circle the ratio of square of radius to area is 1:pi​

Answer 1

Answer:

When a circle is inscribed within a square, its diameter (D) is the same length as the side of the square, and the radius (R) is half that length. Since the area of the circle is PI times the square of R, and the area of the square is FOUR times the square of R (or D^2, which is the square of 2R), the ratio of the areas is: [math] \frac {\pi} {4} .[/math]

When a square is inscribed within a circle, the diagonal of the square (D) is also the diameter of the circle. Since the diagonal of the square is [math]\sqrt {2} [/math]times the the length (S) of its side, the side is [math] \frac {D} {\sqrt{2}} = \frac{D * \sqrt{2}}{2} [/math] and the area of the square is the square of that, or [math] 2 * D^2 . [/math] Thus, the ratio of areas of the circle and square is [math] \frac {\pi} {2}[/math] , when the former is inscribed within the latter.

Note that the area of the inscribed square is half the area of the circumscribed square.

Step-by-step explanation:

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